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Could we use gravitational models to predict urban growth? The idea is that humans are attracted to cities just like space rocks are attracted to bigger celestial bodies, because of the gravitational law - and that's how the biggest stars were eventually created. Maybe the same exact law applies:

  • Attraction is inversely proportional to square of the distance (between city and individual)
  • Attraction is proportional to the size of the city

Of course, there's one more big causal element in urban growth: population growth. Is this factor a better predictor than the propensity of human beings to cluster together - certainly not in places like Europe where growth has stopped, yet urban growth has not (exodus from rural areas is still strong). I don't think we have more matter being produced in the universe: according to physicists, the amount of matter is fixed. So the fact that celestial bodies grew bigger and bigger then merged, created planets, stars and their satellites, is entirely caused by the force of (gravitational) attraction. But initially these rocks were isolated and scattered all over, just like humans in prehistoric times.

To add to the analogy, the growth process does not end up with one gigantic city and nothing outside that city, but instead, we eventually reach an equilibrium point with

  • A few giant cities, like mega-stars 100 times bigger than our sun (I'd be curious to know the proportion of total visible matter stored in these stars; also, what's the proportion of humans living in these mega-cities like Tokyo, Shanghai, Mexico, New York?)
  • Many very big cities (Paris), comparable to stars like our sun
  • Smaller cities (Seattle, comparable to Jupiter)
  • Towns, comparable to planets and satellites
  • Very small, rural human communities, comparable to lone space rocks on the loose

You could go one step further and claim that there's a limit to growth, just like for stars. At a certain point, when a star gets too big, it blows up. It's not difficult to imagine the same thing happening to a city that goes beyond a certain point - 50 million human beings packed on a 2500 square mile area (with tall skyscrapers it's 3D, not 2D) will eventually collapse under its own weight (massive disease, terrorism, too expensive to manage, food problems, etc. whatever it is, from a macroscopic point of view, it's similar to the collapse of a mega-star).  

Of course, unlike physical laws, the law of urban attraction is subject to significant statistical variations, thus you need statistical modeling if you want to apply these laws to human behavior, to make predictions.

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Would be interesting to see a model (simulation or projections for 2013-2100) where urban areas grow at the expense of rural areas, maybe as a video that shows how the clusters (cities) get created, evolve and merge over time. And compare with real data that show growth over time on a map - say between 1900 and 2000.. 

Here's another interesting model, not sure how it relate to yours: The Dynamic of Spain's Population Follows the Maximum Entropy Princ....

Also, stars are not the bigger clusters created by gravitation. Star clusters, galaxies and galaxy clusters are even bigger and might collapse into black holes if they become too big / too compact or if all energy is burned up.

"Could we use gravitational models to predict urban growth?"

Sure we could. In fact we have already done it ... nearly half a century ago. Gravity models aka Spatial Interaction Models include some of the first urban growth models such as the Lowry model (Lowry 1964), MEPLAN (Abraham 1998) and Tranus (Vichiensan 2003).

Concerning the visualization part, it is indeed extremely fascinating, especialy when the results capture not only the spatial extend of urban growth but as wells as the change in the intensity of urbanization in already urban areas.

An excelent point Vincent! 

@Mantelas: Today, thanks to big computers and the cloud, we can make massive simulations.

So Vince, gravity models have been used in urban and regional economics aka urban and regional science--another discipline that emerged in the later half of the 20th, and wanted to demarcate itself as a science--for decades in its research program and in the accompanying outpouring of empirical and theoretical literature. That's why I always tell the IT creeps that if they want to read something new they ought to pick up an old book.

Vince, I'd like very much to talk with you. I'm not sure where you really stand in what I now call the big data mess, but I detect some recent change in your stance, perhaps moving away gradually from inherently and fundamentally IT-centric definitions and use cases of "data science" and "data scientist."

I'm still disturbed, however, by yours, Davenport's, and a host of other Wired Mag/Rag IT types' view that analysis is 95 percent data management and maybe 5 percent "analysis." And "analysis", such as it is, is itself bounded by an IT-centric field that does not admit of the need for subject matter experts, like the economist/econometrician or other organizational /behavioral scientist who has theoretical frameworks and emerging hypotheses that can be tested better, and much better, with access to more and better big data. The result is that many if not most of the analytical products, the eventual deliverables of any research effort in the business world, are stunted, in that they do not extract the maximum possible information from the data at hand. And "analytics"--the ugly name that surely no one will ever steal--becomes just another failed IT-effort, with SME analysts taking collateral damage. That's damnably unfair because it was always IT driving the bus, and the SME analysts were in the back, marginalized by all the geeks.

I'd like to talk to you about putting the analysts first, or more properly, at the head table, with an equally decisive voice in establishing the framework of business-analytic research projects. NOT beginning with which choice of software, but with decisions about what the research question is, really, all about. THEN the decision about which data to look at, and so on, thereby establishing a protocol for the work of the analyst that is at least as rigorous, if not more than, the determination of requirements in a software engineering project.

What do you think? Really interested in your thoughts. I'm at 571-271-2184, or [email protected] 

Also, you can see how gravity models work, in exquisite detail, if/when you ever get to play around with the REMI Model, of Amherst, MA, a CGE model, coupled with a national-regional econometric forecasting and simulastion model, on top of a robust I-O platform.

Bill Luker

It is part of my dissertation and also some intern work I have done in the past for a utility company. We used cellular automata and agent-based model to simulate urban change, from the bottom level up. It is indeed computationally intensive but the result is really fascinating. Urban growth outward and inward (like gentrification or inner city renovation) is driven by individual real estate developers and home-buyers and a number of physical and socioeconomic conditions, so this bottom-up simulation framework can do much better than macroscopic models like gravity or entropy maximization.  Research in this topic has been very active for 20 years and now we are lucky to use current urban maps to validate models created 20 years ago. Simulation, machine learning, and data mining are all applied in this research field and right now we can get predictive accuracy between 80% - 90%. Also to note, this work has been done at many parts of the world, both developed and developing countries. 

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